Wavefront optimization for tuning scanner based on performance matching

Abstract

A method for determining a wavefront parameter of a patterning process. The method includes obtaining a reference performance (e.g., a contour, EPE, CD) of a reference apparatus (e.g., a scanner), a lens model for a patterning apparatus configured to convert a wavefront parameter of a wavefront to actuator movement, and a lens fingerprint of a tuning apparatus (e.g., a to-be-matched scanner). Further, the method involves determining the wavefront parameter (e.g., a wavefront parameter such as tilt, offset, etc.) based on the lens fingerprint of the tuning apparatus, the lens model, and a cost function, wherein the cost function is a difference between the reference performance and a tuning apparatus performance.

What is claimed is: 
     
       1. A method comprising:
 obtaining (i) a weight map associated with an exposure wavefront, wherein weights of the weight map are associated with a performance metric of a patterning apparatus, and (ii) a lens model configured to convert an aberration wavefront parameter associated with the exposure wavefront to a lens adjustment parameter; 
 determining, via executing the lens model using the weight map and the exposure wavefront, a lens adjustment parameter value such that a lens model merit function associated with the lens model is improved, wherein the lens model merit function is a function of the weight map; and 
 adjusting, via simulating a patterning process using an aberration wavefront associated with the lens adjustment parameter value, weights of the weight map such that the performance metric of the patterning process is improved, the performance metric being a function of an edge placement error and a pattern placement error associated with a pattern to be printed on a substrate. 
 
     
     
       2. The method of  claim 1 , wherein the weight map is a pixelated image, wherein a given pixel of the pixelated image is assigned a weight based on an impact of change in the given pixel value on the performance metric. 
     
     
       3. The method of  claim 1 , wherein weights of the weight map are based on diffraction information associated with an illumination pupil, wherein the diffraction information comprises diffraction orders and/or a diffraction intensity pattern. 
     
     
       4. The method of  claim 1 , wherein weights of the weight map are based on Zernike sensitivities, a given Zernike sensitivity being a partial derivative of the performance metric with respect to a given Zernike polynomial. 
     
     
       5. The method of  claim 1 , wherein weights of the weight map are based on principal component analysis (PCA) of a set of wavefronts, the set of wavefronts obtained from one or more lithographic apparatuses used in the patterning process. 
     
     
       6. The method of  claim 1 , wherein the determining of the lens adjustment parameter is an iterative process, an iteration comprising:
 executing the lens model using the weight map and the given exposure wavefront to generate the aberration wavefront; 
 determining, based on the aberration wavefront, the edge placement error and the pattern placement error associated with one or more portions of the aberration wavefront; 
 evaluating the performance metric using the edge placement error and the pattern placement error; and 
 adjusting, via lens actuator adjustment, the aberration wavefront parameter based on a gradient of the performance metric such that the performance metric is improved. 
 
     
     
       7. The method of  claim 1 , further comprising:
 de-weighting or upweighting a region of an illumination pupil via the weight map; 
 executing the lens model using the de-weighted weight map or the upweighted weight map; and 
 determining another lens adjustment parameter value associated with the aberration wavefront using the de-weighted weight map or the upweighted weight map, and the exposure wavefront associated therewith so that the performance metric is minimized. 
 
     
     
       8. The method of  claim 1 , wherein the lens model merit function is minimized. 
     
     
       9. The method of  claim 1 , wherein the lens model includes constraints related to correction limitations of the patterning apparatus corresponding to the aberration wavefront. 
     
     
       10. The method of  claim 1 , wherein the exposure wavefront is a through-slit wavefront. 
     
     
       11. The method of  claim 1 , further comprising:
 converting, via the lens model, the aberration wavefront parameter to the lens adjustment parameter; and 
 actuating an optical system of a patterning apparatus based on the lens adjustment parameter. 
 
     
     
       12. A computer readable non-transitory storage medium comprising instructions, the instructions, when executed by a computer system, configured to cause the computer system to at least:
 obtain (i) a weight map associated with an exposure wavefront, wherein weights of the weight map are associated with a performance metric of a patterning apparatus, and (ii) a lens model configured to convert an aberration wavefront parameter associated with the exposure wavefront to a lens adjustment parameter; 
 determine, via execution of the lens model using the weight map and the exposure wavefront, a lens adjustment parameter value such that a lens model merit function associated with the lens model is improved, wherein the lens model merit function is a function of the weight map; and 
 adjust, via simulation of a patterning process using an aberration wavefront associated with the lens adjustment parameter value, weights of the weight map such that the performance metric of the patterning process is improved, the performance metric being a function of an edge placement error and a pattern placement error associated with a pattern to be printed on a substrate. 
 
     
     
       13. A method of determining lens actuator setting for a patterning apparatus, the method comprising:
 obtaining a lens merit function and a reference value assigned to a residual aberration wavefront associated with the patterning apparatus; and 
 determining, via a lens model of the patterning apparatus using the lens merit function and the reference value, the lens actuator setting from a lens actuator space of the patterning apparatus based on evaluating the lens merit function, the lens merit function comprising a lithographic metric associated with the residual aberration wavefront. 
 
     
     
       14. The method of  claim 13 , wherein the lens merit function is determined based on a lithographic merit function, the lithographic merit function comprising:
 an edge placement error associated with a pattern to be imaged on a substrate; and 
 a pattern placement error, the pattern placement error being a mutual shift of features in a layer, the mutual shift being relative to a reference position on the substrate. 
 
     
     
       15. The method of  claim 14 , wherein the reference value is associated with one or more points at or around a global minimum of the lithographic merit function. 
     
     
       16. The method of  claim 13 , wherein the lithographic metric is a function of at least 2 nd  order of edge placement error (EPE) and/or at least 2 nd  order of pattern placement error (PPE), wherein the EPE and/or the PPE are caused due to changes in the lens actuator setting. 
     
     
       17. The method of  claim 13 , wherein the lithographic metric defines a hyperplane in the lens actuator space, the hyperplane providing a relationship between the lithographic metric and at least two actuator settings of the lens actuator space. 
     
     
       18. The method of  claim 13 , wherein the determining of the lens actuator setting is an iterative process, an iteration comprises:
 executing the lens model using a sub-set of the lens actuator space to determine an aberration wavefront; 
 determining, using the determined aberration wavefront, the lithographic metric and the lens merit function; 
 determining a gradient of the lens merit function and/or the lithographic metric with respect to the lens actuator space; and 
 selecting, based on the gradient of the lens merit function and/or the lithographic metric, another subset of the lens actuator space that causes the lens merit function and/or the lithographic metric to be reduced in a subsequent iteration. 
 
     
     
       19. The method of  claim 13 , wherein the lithographic metric is a function of sensitivities of the residual aberration wavefront and/or a measured wavefront associated with a given lens actuator setting, the sensitivities being determined with respect to a merit function of the patterning process. 
     
     
       20. A computer readable non-transitory storage medium comprising instructions, the instructions, when executed by a computer system, configured to cause the computer system to at least:
 obtain a lens merit function and a reference value assigned to a residual aberration wavefront associated with a patterning apparatus; and 
 determine, via a lens model of the patterning apparatus using the lens merit function and the reference value, a lens actuator setting from a lens actuator space of the patterning apparatus based on evaluation of the lens merit function, the lens merit function comprising a lithographic metric associated with the residual aberration wavefront.